diff --git a/eigen3/include/ignition/math/eigen3/Util.hh b/eigen3/include/ignition/math/eigen3/Util.hh
new file mode 100644
index 000000000..25f740bd8
--- /dev/null
+++ b/eigen3/include/ignition/math/eigen3/Util.hh
@@ -0,0 +1,161 @@
+/*
+ * Copyright (C) 2021 Open Source Robotics Foundation
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+*/
+
+#ifndef IGNITION_MATH_EIGEN3_UTIL_HH_
+#define IGNITION_MATH_EIGEN3_UTIL_HH_
+
+#include <vector>
+
+#include <Eigen/Geometry>
+#include <Eigen/Eigenvalues>
+
+#include <ignition/math/AxisAlignedBox.hh>
+#include <ignition/math/Matrix3.hh>
+#include <ignition/math/OrientedBox.hh>
+#include <ignition/math/Pose3.hh>
+#include <ignition/math/Quaternion.hh>
+#include <ignition/math/Vector3.hh>
+#include <ignition/math/eigen3/Conversions.hh>
+
+namespace ignition
+{
+  namespace math
+  {
+    namespace eigen3
+    {
+      /// \brief Get covariance matrix from a set of 3d vertices
+      /// https://github.com/isl-org/Open3D/blob/76c2baf9debd460900f056a9b51e9a80de9c0e64/cpp/open3d/utility/Eigen.cpp#L305
+      /// \param[in] _vertices a vector of 3d vertices
+      /// \return Covariance matrix
+      inline Eigen::Matrix3d covarianceMatrix(
+        const std::vector<math::Vector3d> &_vertices)
+      {
+        if (_vertices.empty())
+          return Eigen::Matrix3d::Identity();
+
+        Eigen::Matrix<double, 9, 1> cumulants;
+        cumulants.setZero();
+        for (const auto &vertex : _vertices)
+        {
+          const Eigen::Vector3d &point = math::eigen3::convert(vertex);
+          cumulants(0) += point(0);
+          cumulants(1) += point(1);
+          cumulants(2) += point(2);
+          cumulants(3) += point(0) * point(0);
+          cumulants(4) += point(0) * point(1);
+          cumulants(5) += point(0) * point(2);
+          cumulants(6) += point(1) * point(1);
+          cumulants(7) += point(1) * point(2);
+          cumulants(8) += point(2) * point(2);
+        }
+
+        Eigen::Matrix3d covariance;
+
+        cumulants /= static_cast<double>(_vertices.size());
+
+        covariance(0, 0) = cumulants(3) - cumulants(0) * cumulants(0);
+        covariance(1, 1) = cumulants(6) - cumulants(1) * cumulants(1);
+        covariance(2, 2) = cumulants(8) - cumulants(2) * cumulants(2);
+        covariance(0, 1) = cumulants(4) - cumulants(0) * cumulants(1);
+        covariance(1, 0) = covariance(0, 1);
+        covariance(0, 2) = cumulants(5) - cumulants(0) * cumulants(2);
+        covariance(2, 0) = covariance(0, 2);
+        covariance(1, 2) = cumulants(7) - cumulants(1) * cumulants(2);
+        covariance(2, 1) = covariance(1, 2);
+        return covariance;
+      }
+
+      /// \brief Get the oriented 3d bounding box of a set of 3d
+      /// vertices using PCA
+      /// http://codextechnicanum.blogspot.com/2015/04/find-minimum-oriented-bounding-box-of.html
+      /// \param[in] _vertices a vector of 3d vertices
+      /// \return Oriented 3D box
+      inline ignition::math::OrientedBoxd verticesToOrientedBox(
+        const std::vector<math::Vector3d> &_vertices)
+      {
+        math::OrientedBoxd box;
+
+        // Return an empty box if there are no vertices
+        if (_vertices.empty())
+          return box;
+
+        math::Vector3d mean;
+        for (const auto &point : _vertices)
+          mean += point;
+        mean /= static_cast<double>(_vertices.size());
+
+        Eigen::Vector3d centroid = math::eigen3::convert(mean);
+        Eigen::Matrix3d covariance = covarianceMatrix(_vertices);
+
+        // Eigen Vectors
+        Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d>
+          eigenSolver(covariance, Eigen::ComputeEigenvectors);
+        Eigen::Matrix3d eigenVectorsPCA = eigenSolver.eigenvectors();
+
+        // This line is necessary for proper orientation in some cases.
+        // The numbers come out the same without it, but the signs are
+        // different and the box doesn't get correctly oriented in some cases.
+        eigenVectorsPCA.col(2) =
+          eigenVectorsPCA.col(0).cross(eigenVectorsPCA.col(1));
+
+        // Transform the original cloud to the origin where the principal
+        // components correspond to the axes.
+        Eigen::Matrix4d projectionTransform(Eigen::Matrix4d::Identity());
+        projectionTransform.block<3, 3>(0, 0) = eigenVectorsPCA.transpose();
+        projectionTransform.block<3, 1>(0, 3) =
+          -1.0f * (projectionTransform.block<3, 3>(0, 0) * centroid);
+
+        Eigen::Vector3d minPoint(INF_I32, INF_I32, INF_I32);
+        Eigen::Vector3d maxPoint(-INF_I32, -INF_I32, -INF_I32);
+
+        // Get the minimum and maximum points of the transformed cloud.
+        for (const auto &point : _vertices)
+        {
+          Eigen::Vector4d pt(0, 0, 0, 1);
+          pt.head<3>() = math::eigen3::convert(point);
+          Eigen::Vector4d tfPoint = projectionTransform * pt;
+          minPoint = minPoint.cwiseMin(tfPoint.head<3>());
+          maxPoint = maxPoint.cwiseMax(tfPoint.head<3>());
+        }
+
+        const Eigen::Vector3d meanDiagonal = 0.5f * (maxPoint + minPoint);
+
+        // quaternion is calculated using the eigenvectors (which determines
+        // how the final box gets rotated), and the transform to put the box
+        // in correct location is calculated
+        const Eigen::Quaterniond bboxQuaternion(eigenVectorsPCA);
+        const Eigen::Vector3d bboxTransform =
+          eigenVectorsPCA * meanDiagonal + centroid;
+
+        math::Vector3d size(
+            maxPoint.x() - minPoint.x(),
+            maxPoint.y() - minPoint.y(),
+            maxPoint.z() - minPoint.z()
+        );
+        math::Pose3d pose;
+        pose.Rot() = math::eigen3::convert(bboxQuaternion);
+        pose.Pos() = math::eigen3::convert(bboxTransform);
+
+        box.Size(size);
+        box.Pose(pose);
+        return box;
+      }
+    }
+  }
+}
+
+#endif
diff --git a/eigen3/src/Util_TEST.cc b/eigen3/src/Util_TEST.cc
new file mode 100644
index 000000000..1e5220462
--- /dev/null
+++ b/eigen3/src/Util_TEST.cc
@@ -0,0 +1,172 @@
+/*
+ * Copyright (C) 2021 Open Source Robotics Foundation
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+*/
+
+#include <gtest/gtest.h>
+
+#include <ignition/math/eigen3/Util.hh>
+
+using namespace ignition;
+
+/////////////////////////////////////////////////
+/// \brief Test the oriented box converted from a set of vertices
+TEST(EigenUtil, verticesToOrientedBox)
+{
+  std::vector<math::Vector3d> vertices;
+
+  vertices.push_back(math::Vector3d(1, 0, 0.5));
+  vertices.push_back(math::Vector3d(2, 0.1, 0.4));
+  vertices.push_back(math::Vector3d(2, 1, 3));
+  vertices.push_back(math::Vector3d(1.6, 0.3, 0.1));
+  vertices.push_back(math::Vector3d(1.5, 0.5, 1));
+  vertices.push_back(math::Vector3d(1.4, 1, 3));
+  vertices.push_back(math::Vector3d(1, 0.4, 0.7));
+  vertices.push_back(math::Vector3d(0.9, 1.3, 0));
+  vertices.push_back(math::Vector3d(0.6, 4, 2));
+  vertices.push_back(math::Vector3d(0, 3, 3));
+  vertices.push_back(math::Vector3d(-1, -2, 4));
+  vertices.push_back(math::Vector3d(-2, -2, 0.6));
+
+  math::OrientedBoxd box = math::eigen3::verticesToOrientedBox(
+    vertices);
+
+  auto position = box.Pose().Pos();
+  auto rotation = box.Pose().Rot();
+  auto size = box.Size();
+
+  double error = 0.1;
+
+  EXPECT_NEAR(size.X(), 3.09, error);
+  EXPECT_NEAR(size.Y(), 4.39, error);
+  EXPECT_NEAR(size.Z(), 6.63, error);
+
+  EXPECT_NEAR(position.X(), 0.38, error);
+  EXPECT_NEAR(position.Y(), 0.47, error);
+  EXPECT_NEAR(position.Z(), 1.96, error);
+
+  EXPECT_NEAR(rotation.Roll(), -1.66, error);
+  EXPECT_NEAR(rotation.Pitch(), 0.4, error);
+  EXPECT_NEAR(rotation.Yaw(), 2.7, error);
+}
+
+/////////////////////////////////////////////////
+TEST(EigenUtil, emptyVertices)
+{
+  std::vector<math::Vector3d> emptyVertices;
+
+  math::OrientedBoxd box = math::eigen3::verticesToOrientedBox(
+    emptyVertices);
+
+  auto position = box.Pose().Pos();
+  auto rotation = box.Pose().Rot();
+  auto size = box.Size();
+
+  EXPECT_DOUBLE_EQ(size.X(), 0);
+  EXPECT_DOUBLE_EQ(size.Y(), 0);
+  EXPECT_DOUBLE_EQ(size.Z(), 0);
+
+  EXPECT_DOUBLE_EQ(position.X(), 0);
+  EXPECT_DOUBLE_EQ(position.Y(), 0);
+  EXPECT_DOUBLE_EQ(position.Z(), 0);
+
+  EXPECT_DOUBLE_EQ(rotation.Roll(), 0);
+  EXPECT_DOUBLE_EQ(rotation.Pitch(), 0);
+  EXPECT_DOUBLE_EQ(rotation.Yaw(), 0);
+}
+
+/////////////////////////////////////////////////
+TEST(EigenUtil, simpleBox)
+{
+  std::vector<math::Vector3d> vertices;
+
+  vertices.push_back(math::Vector3d(-1, -1, -1));
+  vertices.push_back(math::Vector3d(-1, 1, -1));
+  vertices.push_back(math::Vector3d(1, -1, -1));
+  vertices.push_back(math::Vector3d(1, 1, -1));
+  vertices.push_back(math::Vector3d(-1, -1, 1));
+  vertices.push_back(math::Vector3d(-1, 1, 1));
+  vertices.push_back(math::Vector3d(1, -1, 1));
+  vertices.push_back(math::Vector3d(1, 1, 1));
+
+  math::OrientedBoxd box = math::eigen3::verticesToOrientedBox(
+    vertices);
+
+  auto position = box.Pose().Pos();
+  auto rotation = box.Pose().Rot();
+  auto size = box.Size();
+
+  double error = 0.1;
+
+  EXPECT_NEAR(size.X(), 2, error);
+  EXPECT_NEAR(size.Y(), 2, error);
+  EXPECT_NEAR(size.Z(), 2, error);
+
+  EXPECT_NEAR(position.X(), 0, error);
+  EXPECT_NEAR(position.Y(), 0, error);
+  EXPECT_NEAR(position.Z(), 0, error);
+
+  EXPECT_NEAR(rotation.Roll(), 0, error);
+  EXPECT_NEAR(rotation.Pitch(), 0, error);
+  EXPECT_NEAR(rotation.Yaw(), 0, error);
+}
+
+/////////////////////////////////////////////////
+TEST(EigenUtil, covarianceTest)
+{
+  std::vector<math::Vector3d> vertices;
+
+  vertices.push_back(math::Vector3d(1, 0, 0.5));
+  vertices.push_back(math::Vector3d(2, 0.1, 0.4));
+  vertices.push_back(math::Vector3d(2, 1, 3));
+  vertices.push_back(math::Vector3d(1.6, 0.3, 0.1));
+  vertices.push_back(math::Vector3d(1.5, 0.5, 1));
+  vertices.push_back(math::Vector3d(1.4, 1, 3));
+  vertices.push_back(math::Vector3d(1, 0.4, 0.7));
+
+  Eigen::Matrix3d covariance = math::eigen3::covarianceMatrix(
+    vertices);
+
+  double error = 0.1;
+
+  EXPECT_NEAR(covariance(0), 0.145714, error);
+  EXPECT_NEAR(covariance(1), 0.04, error);
+  EXPECT_NEAR(covariance(2), 0.115714, error);
+  EXPECT_NEAR(covariance(3), 0.04, error);
+  EXPECT_NEAR(covariance(4), 0.136327, error);
+  EXPECT_NEAR(covariance(5), 0.392653, error);
+  EXPECT_NEAR(covariance(6), 0.115714, error);
+  EXPECT_NEAR(covariance(7), 0.392653, error);
+  EXPECT_NEAR(covariance(8), 1.29959, error);
+}
+
+/////////////////////////////////////////////////
+TEST(EigenUtil, covarianceEmptyTest)
+{
+  std::vector<math::Vector3d> vertices;
+
+  Eigen::Matrix3d covariance = math::eigen3::covarianceMatrix(
+    vertices);
+
+  EXPECT_DOUBLE_EQ(covariance(0), 1);
+  EXPECT_DOUBLE_EQ(covariance(1), 0);
+  EXPECT_DOUBLE_EQ(covariance(2), 0);
+  EXPECT_DOUBLE_EQ(covariance(3), 0);
+  EXPECT_DOUBLE_EQ(covariance(4), 1);
+  EXPECT_DOUBLE_EQ(covariance(5), 0);
+  EXPECT_DOUBLE_EQ(covariance(6), 0);
+  EXPECT_DOUBLE_EQ(covariance(7), 0);
+  EXPECT_DOUBLE_EQ(covariance(8), 1);
+}